More Fun With Ratios

Well, since the last ratios problem seemed to be such a huge hit, I thought you guys might like another one. This ratios problem is not really mathematically that much more difficult than any other, but the wording of the problem sometimes gives people fits. I often find that the most difficult part of any math problem on any standardized test is not the actual math but the translation from word problem to math problem. Anyway, here it is.

Jonathan needs to mix 1 part bleach for every 5 parts water to make his cleaning solution. While he’s mixing the solution, he makes a mistake and mixes in half as much bleach as he should have. The total solution is 44 mL. How much bleach did Jonathan put into the solution?

Let’s get straight to it. We know two things about the solution:Roblox Robux Hack 2017

  1. The total volume of the solution is 44 mL.
  2. The ratio of bleach to water is 0.5:5

Notice the ratio. The problem says that the solution is supposed to be 1:5 bleach to water, but Jonathan makes a mistake and uses half as much bleach as he should. That’s where the 0.5 comes from.

Now, we just use the same method as last time to solve the system of equations.

  1. B + W = 44
  2. B/W = 0.5/5 = 1/10

The ratio of 0.5:5 is the same as 1:10 (just multiply both the top and bottom by 2).

Solving for B in the second equation, we get

B = W/10

Plugging in and solving, we get

W/10 + W = 44     (substitution)
W/10 + 10W/10 = 44     (find common denominator)
11W/10 = 44     (combine like terms)
11W = 440     (multiply both sides by 10)
W = 40     (divide both sides by 11)

Jonathan put 40 mL of water in the solution, but the question is asking about bleach, so we just subtract 40 mL from 44 mL, and we get 4 mL of bleach.

As you can see, the math for this problem is the same as before. The only tricky part was figuring out how to translate the word problem into the math problem. In this example, all we had to do was change the ratio to match what the problem described. Jonathan put half as much bleach in as he was supposed to, so we just alter the ratio to use half as much bleach. Then, the question proceeds exactly the same as any other.

Stay tuned — next time we’ll go over a much more difficult ratios problem.

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